Q&A - PSLE Math

[ADoc]

peggy:

Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

Hi! Other than algebra, which some primary students may not be too comfortable with, we explain to them that before we can compare ratio or fraction units of the SAME qty, we must change them to the same number of units. This is an important concept in order to score those ratio qs, that I'm sure parents and students here are already very familiar with.

(2/3) x 3 = 6/9 } ali
(3/5) x 2 = 6/10 } raju

We see that Ali has 1 unit less than raju ---> 100 books
therefore Ali has 9 x 100 = 900 books.

Another variation of this sort of 2-mark qs is to ask for the fraction or ratio of say, Ali's to raju's.

cheers
eugene

[ADoc]

http://i42.tinypic.com/zbp0o.jpg\">


Hi! A couple of good practices to enhance our kids' understanding for this type of qs:

(1) explain to the kid the concept of finding the area of a fraction of a circle

Our primary students are familiar with area of semi-circles ( x 1/2) and quadrants ( x 1/4). To reinforce their understanding, we explain to them the \"whys\": half a circle is 180 deg --> what fraction is 180 deg of a full circle? --> 180/360 = 1/2 --> that's why we multiply 1/2 for area of semi-circle. Similar explanation for quadrants. Now we can stretch this understanding and explain to them that for any part of a circle, so long as we know the angle that it subtends, say 45 deg in this example, it is 45/360 = 1/8 of a circle.

(2) do not be afraid to add in extra alphabets (or points) on the figure if it helps you to understand this sort of plus and minus areas of various shapes problem.

In this example: adding a point F, where the arc BE and Line DC intersect, may be useful.

So we have:
area of part of a circle ABE = area of shaded part ADFE + area of BDF
area of triangle BCD = area of shaded part BCF + area of BDF

Now perhaps our kids can see the solution clearer. Qs asks for difference between the shaded areas, hence it's area of part of a circle ABE minus area of triangle BCD, since the area of BDF cancels out each other.

Sorry for the wordy explanation. These are meant to help parents to explain to their kids should they face difficulty.

Hope this is useful to some.

cheers
eugene

[ADoc]

jewelbox:

http://i42.tinypic.com/2vx51tx.jpg\">

Hi! Again, without using formal algebra as our kids may be uncomfortable with, we can choose to work simply with ratios that they are well-trained at.

A recurring concept for most, if not all, ratio problems (including fractions), is to change to equivalent ratios. Second is to IDENTIFY the qty that remains constant.

In this case we can choose either (1) the shaded area that is cut is the SAME for both Rect and Sq, or (2) the difference between the areas of the Rect and Sq remains the SAME if we cut the same amount of area from each of them.

Before cutting
R : S = 5 : 2

After cutting
R : S = 3 : 1

using (2) we see that the difference in areas of R and S before and after cutting must remain the SAME as the same qty was cut.

Now we check:

before cutting: R - S = 5 - 2 = 3 units
after cutting: R - S = 3 - 1 = 2 parts [not the same]

the all-too-familiar step is to cross multiply each other:

so we have:

before cutting R : S = 5 : 2 = 10 : 4 (MULTIPLY throughout by \"2\")
after cutting R : S = 3 : 1 = 9 : 3 (MULTIPLY throughout by \"3\")

indeed now the difference in units are the SAME = 6 units

area of S before cutting = 4 units --> 36 cm square
after cutting = 3 units => shaded area = 1 unit
1 unit -- > 9 cm square

again sorry for the lengthy reply. These are meant to guide our kids in their understanding. The workings are much much shorter than these certainly.

For experienced primary students, this should be at most a 4-5min qs as the steps involved are simple.

hope this is useful

cheers
eugene

[peggy]

Hi,


Thanks!

[tianzhu]

jewelbox:

Thanks Tianzhu, you are fast. I will slowly digest your solutions. Meanwhile i have prob solving this qn. Thanks. http://i42.tinypic.com/zbp0o.jpg\">

Hi

Good Morning.

Imagine you are seeing a reflection of the picture or image. Flip the image so that you can see a square formed by the two isoceles triangles.

Find the area of (Area of quadrant – Area of isosceles triangle) and divide it by 2.

Area of quadrant ------ 38.5

Area of isosceles triangle ------ 24.5

38.5 – 24.5 ------14

Difference in shaded area ----- 14 /2 ------ 7

Best wishes

[mathnoobs]

tianzhu:

jewelbox:

Thanks Tianzhu, you are fast. I will slowly digest your solutions. Meanwhile i have prob solving this qn. Thanks. http://i42.tinypic.com/zbp0o.jpg\">

Hi

Good Morning.

Imagine you are seeing a reflection of the picture or image. Flip the image so that you can see a square formed by the two isoceles triangles.

Find the area of (Area of quadrant – Area of isosceles triangle) and divide it by 2.

Area of quadrant ------ 38.5

Area of isosceles triangle ------ 24.5

38.5 – 24.5 ------14

Difference in shaded area ----- 14 /2 ------ 7

Best wishes

Hi Tianzhu
I'm afraid I'm a bit weak in geometry. Hard to visualize things.
I can see the area of a quadrant, which is 1/4 of area of circle, radius 7cm. I can also see the area of isosceles triangle, which is 1/2 area of square.
But I don't see how (area of quadrant - area of triangle)/2 leads to difference in the 2 shaded regions.

[tianzhu]

mathnoobs:

Hi Tianzhu

I'm afraid I'm a bit weak in geometry. Hard to visualize things.
I can see the area of a quadrant, which is 1/4 of area of circle, radius 7cm. I can also see the area of isosceles triangle, which is 1/2 area of square.
But I don't see how (area of quadrant - area of triangle)/2 leads to difference in the 2 shaded regions.

Hi

You're on the right track as you can see the quadrant and isosceles triangle.

I'll prepare the sketch to show you how (area of quadrant - area of triangle)/2 leads to difference in the 2 shaded regions.

Watch your PM.Please give me some time.

Best wishes

[Zack7]

ADoc:

peggy:

Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

Hi! Other than algebra, which some primary students may not be too comfortable with, we explain to them that before we can compare ratio or fraction units of the SAME qty, we must change them to the same number of units. This is an important concept in order to score those ratio qs, that I'm sure parents and students here are already very familiar with.

(2/3) x 3 = 6/9 } ali
(3/5) x 2 = 6/10 } raju

We see that Ali has 1 unit less than raju ---> 100 books
therefore Ali has 9 x 100 = 900 books.

Another variation of this sort of 2-mark qs is to ask for the fraction or ratio of say, Ali's to raju's.

cheers
eugene

your method is quite unorthodox i must say...

firstly, (2/3) x 3 = 2, not 6/9. same with 3/5

secondly, 6/9 is not 1 unit less than 6/10... in fact, 6/9 > 6/10. it might work as a shortcut in this question, but i don't think it is clear to the kids or even the right concept.

a clearer way would be

2/3 ali = 3/5 raja (as per the question)
ali = 9/10 raja (cross multiply)

now here comes the crucial step namely, how to interpret the above equation.
the equation tells you ali has only 9/10 as many books as raja.
always ask yourself when you are forming your conclusion, who has more books who has less. does it agree with the question? in this case, ali has less.

the equation might look like raja has fewer since there is a 9/10 factor, but this is not true because of the equal sign. it is important to note the equality sign.

so in this case, one should interpret it as : the WHOLE of ali is only EQUAL to 9/10 of raja. that means everything that ali has is not even equal to the whole of raja, but rather only equal to 9/10 of raja's books.

so this means 1/10 of raja's books is the amount that is more than ali. so ali has 100 books less than raja, which means raja has 100 more than ali.

9/10 of raja, which is = ali, is then 100x9 = 900.

[Michaelia0816]

Ok now I need help! Pls help!

Question:
A) Mr Chan had a total of 160 pieces of $2 notes and $5 notes. He gave 50% of the $2 notes and 25% of the $5 notes to Susan and had 92 notes left.
a) Find the percentage of the number of $2 notes at first.
b) How much money did Mr Chan have at first?
B) A shopkeeper had some apples and oranges. If 34 apples were sold, the ratio of the number of apples to the number of oranges would be 3:1. If 85 oranges were sold, the ratio would be 29:4. How many apples did he have? :thankyou:

[Zack7]

Michaelia0816:

Ok now I need help! Pls help!

Question:
Mr Chan had a total of 160 pieces of $2 notes and $5 notes. He gave 50% of the $2 notes and 25% of the $5 notes to Susan and had 92 notes left.
a) Find the percentage of the number of $2 notes at first.
b) How much money did Mr Chan have at first?

let x be no. of $2 notes, y be $5

x+y = 160
0.5 x + 0.25 y = 68

2 equations 2 unknowns, you can solve it.

answer should be 70% and $464

part b)

x be apples, y be oranges

x - 34 = 3y
4x = 29( y- 85)

solve

answer should be 493 apples 153 oranges